Convergence acceleration of logarithmically convergent series avoiding summation

Quite often in application, logarithmically convergent series have to be ev aluated. There are several convergence acceleration methods that are based on the evaluation of partial sums s(n) for relatively large n, and thus, no rmally require the evaluation of all terms a(j) with 0 less than or equal t o j less than or equal to n. Here, we show that it is possible to avoid the computation of the partials sums of high order if it is possible to evalua te a few terms a(j) for relatively large j. The effectiveness of the approa ch is demonstrated for the 1/z expansion that is a particularly difficult e xample of logarithmic convergence. (C) 1999 Elsevier Science Ltd. All right s reserved.